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Recent problems solved by 'stanbon'

stanbon answered: 57322 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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Linear-equations/398034: A semiconductor manufacturer seeks to maximize its profits. Testing indicates that they can produce 100,000 chips per week at a cost of $40 per chip, and sell them for $65 per chip. They also find that they can produce 125,000 chips per week at a cost of $35 per chip, and sell them for $63 per chip. How much profit can they expect to earn if they produce 130,000 chips per week? 1 solutions Answer 282053 by stanbon(57395)   on 2011-01-21 22:32:05 (Show Source): You can put this solution on YOUR website! Testing indicates that they can produce 100,000 chips per week at a cost of $40 per chip, and sell them for $65 per chip. They also find that they can produce 125,000 chips per week at a cost of $35 per chip, and sell them for $63 per chip. How much profit can they expect to earn if they produce 130,000 chips per week? ------------- You have two points relating production and profit: (100000,25) and (125000,28) --- slope = (28-25)/(125k-100k) = 3/25k = 0.00012 --------------------- Form: y = mx+b 25 = (0.00012)(10000) + b 25 = 33+b b = -8 -------- Equation: f(x) = (0.00012)x-8 How much profit can they expect to earn if they produce 130,000 chips per week? --- f(130000) = (0.00012)(130000) - 8 f(130000) = 15.6-8 = $7.60 ----------------------------- Cheers, Stan H.

Evaluation_Word_Problems/398031: your weekly paycheck is 30% less then your co worker your two paychecks total 740 find the amount of each paycheck 1 solutions Answer 282039 by stanbon(57395)   on 2011-01-21 22:02:05 (Show Source): You can put this solution on YOUR website! your weekly paycheck is 30% less then your co worker. your two paychecks total 740 find the amount of each paycheck ---- Let one of the paycheck be "x". --- The other paycheck is "0.7x". --- Equation: x + 0.7x = 740 1.7x = 740 x = $435.29 (one of the paychecks) 0.7x = 0.7*435.29 = $304.71 (the other paycheck) ================== Cheers, Stan H.

Rational-functions/398024: Find all numbers for which the rational expression is undefined. (use a comma to separate answers) (t^3-4t)/(t^2-36) 1 solutions Answer 282037 by stanbon(57395)   on 2011-01-21 21:54:33 (Show Source): You can put this solution on YOUR website! Find all numbers for which the rational expression is undefined. (use a comma to separate answers) (t^3-4t)/(t^2-36) ------ The denominator cannot be zero. Solve t^2-36 = 0 (t-6)(t+6) = 0 t = 6 or t = -6 ---- Domain: All Real numbers except t=6 or t=-6 ================== Cheers, Stan H.

Permutations/397989: What is the probability that if you rearranged the letters in the word TURKEY, you would get a “word” that starts with R and ends with a vowel? I tried two ways to get the answer and I don't know which is correct. 1) (1/6) * (2/5) = 1/15 2) ((C (6.1) * C(5.2)) / 6! = 1/12 Are either of these correct? 1 solutions Answer 282012 by stanbon(57395)   on 2011-01-21 19:59:45 (Show Source): You can put this solution on YOUR website! What is the probability that if you rearranged the letters in the word TURKEY, you would get a “word” that starts with R and ends with a vowel? --- Notice: 6 letters; 1 R ; 2 vowels ------- #of ways to "succeed": 1st letter: 1 way last letter: 2 ways 2nd-5th letter: 4*3*2*1 = 24 ways --- # of ways to succeed = 1*2*24 = 48 ---- Total # of possible arrangements: 6! = 720 -- Prob of event as described = 48/720 = 1/15 =============================================== Cheers, Stan H.

test/397994: S.J has 2 jobs offers at as a car salesperson. With the 1st one she will receive $600 per mth plus a 2% commission of the total sale of the automobiles she sells. At the other dealership, she will receive $1000 per mth plus a commission of 1.5% of her total sales. 34.which is the total sale of the automobiles that Ms. J must sell each mth to make the same income from either dealership? 35. Explain which job is better. 1 solutions Answer 282004 by stanbon(57395)   on 2011-01-21 19:22:18 (Show Source): You can put this solution on YOUR website! Ms.J has 2 jobs offers as a car salesperson. With the 1st one she will receive $600 per mth plus a 2% commission of the total sale of the automobiles she sells. --- 1st(x) = 600 + 0.02x ---------------------------------------- At the other dealership, she will receive $1000 per mth plus a commission of 1.5% of her total sales. --- 2nd(x) = 1000 + 0.015x ---------------------------------------- 34.which is the total sales of the automobiles that Ms. J must sell each mth to make the same income from either dealership? --- Solve: 1st(x) = 2nd(x) 600 + 0.02x = 1000 + 0.015x 0.005x = 400 x = 80,000 (break even point) -------------------------------------------- 35. Explain which job is better. I'll leave that to you. Compare the two programs based on x = 70,000 Which one provides the higher Income? --- You could also graph the two plans on the same coordinate system and draw a conclusion. ============================================ Cheers, Stan H.

Permutations/397991: A baseball manager chooses his lineup 1-9. How many ways can he organize his lineup if the pitcher doe not hit in the first four? I did 9*8*7*6*6*5*4*3*2 is this correct? 1 solutions Answer 281996 by stanbon(57395)   on 2011-01-21 19:01:55 (Show Source): You can put this solution on YOUR website! A baseball manager chooses his lineup 1-9. How many ways can he organize his lineup if the pitcher does not hit in the first four? I did 9*8*7*6*6*5*4*3*2 ----- Since the pitcher is not in the 1st four, 8 ways to choose 1st 7 ways to choose 2nd 6 ways to choose 3rd 5 ways to choose 4th 5 ways to choose 3rd 4 ways 3 ways 2 ways 1 ways ============================= Cheers, Stan H.

Linear_Algebra/397982: can you please explain how you work these out. i would be gratful if you show your working out clearly so that i understand it. 2) multiply and simplify : x(2x+8)-x(x-3) 2π(R^2 -r ^2) factorise common factor: 20x - 35 2x^2 +6 12y^2 - 4YX+20x^2Y 2πrh + 2πr^2 solve the follwoing equations 2(x-1)=3 7r+2=5(r-4) Solve simultaneous equations algebraically and draw a graph. a)Y = 2x Y= x + 5 b)3x + y = 13 2x – 3y = 6 c)2x + 3y = 7 3x – 2y = 17 1 solutions Answer 281993 by stanbon(57395)   on 2011-01-21 18:52:22 (Show Source): You can put this solution on YOUR website! multiply and simplify : x(2x+8)-x(x-3) = 2x^2+8x-x^2+3 = x^2+8x+3 --------------------------------------- 2π(R^2 -r ^2) = 2(pi)(R-r)(R+r) --------------------------------------- Factorise common factor: 20x - 35 = 5(4x-7) -------------------------- 2x^2 +6 = 2(x^2+3) -------------------------- 12y^2 - 4YX+20x^2Y = 4(3y^2-xy+5x^2) -------------------------- 2πrh + 2πr^2 = 2(pi)r(h+r) -------------------------- solve the following equations 2(x-1)=3 (x-1) = 3/2 x = 1+(3/2) x = 5/2 -------------------------- 7r+2=5(r-4) 7r+2 = 5r-20 2r = -22 r = -11 -------------------------- Solve simultaneous equations algebraically and draw a graph. a)Y = 2x Y= x + 5 --- Substitute for y and solve for "x": 2x = x + 5 x = 5 --- Then y = 2x = 2*5 = 10 Solution (5,10) -------------------------------------------- b)3x + y = 13 2x – 3y = 6 --- Multiply thru the 1st equation by 3 to get: 9x+3y = 39 2x-3y = 6 ---- Add and solve for "x": 11x = 45 x = 45/11 ------ Solve for "y": 3x + y = 13 3(35/11) + y = 13 (105/11) + y = (13*11/11) y = 38/11 --= -------------------------------------------------------- c)2x + 3y = 7 3x – 2y = 17 --- Multiply thru 1st by 3. Multiply thru 2nd by 2. --- 6x + 9y = 21 6x - 4y = 34 --- Subtract and solve for "y": -13y = 13 y = -1 --- Solve for "x": 2x+3y = 7 2x+3(-1) = 7 2x = 10 x = 5 ---------- ==================== Cheers, Stan H.

Polynomials-and-rational-expressions/397976: It takes 7 hours for 8 cooks to prepare the food for a wedding rehearsal dinner. How long will it take 3 cooks to prepare the dinner? Also what kind variation (inverse or direct) applies to the situation? 1 solutions Answer 281985 by stanbon(57395)   on 2011-01-21 17:53:27 (Show Source): You can put this solution on YOUR website! It takes 7 hours for 8 cooks to prepare the food for a wedding rehearsal dinner. How long will it take 3 cooks to prepare the dinner? Also what kind variation (inverse or direct) applies to the situation? --- The more cooks there are, the less time it takes. t = k/n where t is time and n is # of cooks. ------------------------------- Inverse variation. --- Solve for "k" using t=7 when n = 8: 7 =k/8 k = 56 ---- Equation: t = 56/n ------------ How long will it take 3 cooks to prepare the dinner? t = 56/3 time = 56/3 = 18 2/3 hrs ============================== Cheers, Stan H.

Polynomials-and-rational-expressions/397974: Find the variation constant and an equation of variation where y varies inversely as x. Also y=7 and x=8? 1 solutions Answer 281982 by stanbon(57395)   on 2011-01-21 17:47:01 (Show Source): You can put this solution on YOUR website! Find the variation constant and an equation of variation where y varies inversely as x. --- y = k/x --- Solve for "k" using y=7 and x=8? Equation for this problem: y = 56/x --- 7 = k/8 --- k = 56 =============== Variation constant = 56 ============================== Cheers, Stan H.

Coordinate-system/397969: Identify two coordinates (or a table of values) that would be used to graph using the intercept method: x + 3y = 6. 1 solutions Answer 281980 by stanbon(57395)   on 2011-01-21 17:43:36 (Show Source): You can put this solution on YOUR website! Identify two coordinates (or a table of values) that would be used to graph using the intercept method: x + 3y = 6. ------------------------ If x = 0, 3y = 6 and y = 2 giving you point (0,2) --- If y = 0, x = 6 giving you point (6,0) =================== Cheers, Stan H.

Polynomials-and-rational-expressions/397965: The number N of aluminum cans used each year varies directly as the number of people P using the cans. If 57 people use 16,473 cans in one year, how many cans are used in a city which has a population of 1,862,000? 1 solutions Answer 281979 by stanbon(57395)   on 2011-01-21 17:38:25 (Show Source): You can put this solution on YOUR website! The number N of aluminum cans used each year varies directly as the number of people P using the cans. If 57 people use 16,473 cans in one year, how many cans are used in a city which has a population of 1,862,000? ------------------------------- N = kP Solve for "k" using "If 57 people use 16,473 cans in one year". 16,473 = k*57 k = 289 --- Equation: N = 289/P --- How many cans are used in a city which has a population of 1,862,000? N = 289/1,862,000 --- N = 1.5521x10^-4 =================== Cheers, Stan H.

Rate-of-work-word-problems/397960: One pump can empty a tank three times as another. working together they can complete a job in four hours, find the rate of each pump 1 solutions Answer 281974 by stanbon(57395)   on 2011-01-21 17:27:36 (Show Source): You can put this solution on YOUR website! One pump can empty a tank three times as another. working together they can complete a job in four hours, find the rate of each pump --- One pump rate: 1/x job/hr Other pump rate: 1/(3x) job/hr ----- Together rate: 1/4 job/hr ================================ Equation: rate + rate = together rate 1/x + 1/(3x) = 1/4 --- Multiply thru by 12x to get: 12 + 4 = 3x 3x = 16 ----- One pump DATA: x = 16/3 hr Pump rate = (3/16) job/hr ----- Other pump DATA: time = 3x = 16 hr Pump rate = 1/16 job/hr ============================= Cheers, Stan H. ============

Polynomials-and-rational-expressions/397957: A particular hybrid car travels approximately 312 miles on 6 gallons of gas. Find the amount of gas required for a 936 mile trip? 1 solutions Answer 281966 by stanbon(57395)   on 2011-01-21 17:13:26 (Show Source): You can put this solution on YOUR website! A particular hybrid car travels approximately 312 miles on 6 gallons of gas. Find the amount of gas required for a 936 mile trip? ------- gas/miles = gas/miles x/936 = 6/312 x = 936(6/312) --- x = 3*6 x = 18 gallons ======================= Cheers, Stan H.

Complex_Numbers/397904: The point (-5+bi) has been plotted on the complex plane and r=9. If 0°≤θ≤180° find the value of b. Leave your answer as a radical. Thank you all for your time and assistance! -ClanMacniall 1 solutions Answer 281945 by stanbon(57395)   on 2011-01-21 16:20:32 (Show Source): You can put this solution on YOUR website! The point (-5+bi) has been plotted on the complex plane and r=9. If 0°≤θ≤180° find the value of b. Leave your answer as a radical. ----------- With that range for theta, (-5+bi) must be in the 2nd Quadrant and b must be positive. ---- x = -5 and r = 9 --- Solve for "y" 9^2 = [5^2+y^2] 81 = 25 + y^2 y^2 = 56 y = sqrt(56) ---- b = y = sqrt(56) =================== Cheers, Stan H.

Rate-of-work-word-problems/397942: elsa can complete a typing job in six hours. She was given a helper and together they finish the job in only four days. How long would it take the helper had he worked alone 1 solutions Answer 281941 by stanbon(57395)   on 2011-01-21 16:12:26 (Show Source): You can put this solution on YOUR website! elsa can complete a typing job in six hours. She was given a helper and together they finish the job in only four hours. How long would it take the helper had he worked alone ------ Elsa rate = 1/6 job/hr Helper's rate = 1/x job/hr Together rate = 1/4 job/hr -------------------------------- Equation: rate + rate = together rate 1/6 + 1/x = 1/4 --- Multiply thru by 12x to get: 2x + 12 = 3x x = 12 hrs (time for helper to do job alone) ============================== Cheers, Stan H.

Complex_Numbers/397891: Hi, I am having a hard time with these two complex numbers problems. Can anyone help? Thanks. Directions: Without using a graph, find the endpoint of the vector that satisfies the following questions. 1. (-5-3i)+(20-7i) 2. (7+8i)-(6+9i) 1 solutions Answer 281940 by stanbon(57395)   on 2011-01-21 16:09:18 (Show Source): You can put this solution on YOUR website! Without using a graph, find the endpoint of the vector that satisfies the following questions. 1. (-5-3i)+(20-7i) = (-5+20)+(-3-7)i = 15-10i ------------------- 2. (7+8i)-(6+9i) = 1-i ====== cheers, Stan H.

real-numbers/397940: iF I have 4x^2+5=6x^3 how would i solve for a real number solutions? 1 solutions Answer 281939 by stanbon(57395)   on 2011-01-21 16:05:28 (Show Source): You can put this solution on YOUR website! 4x^2+5=6x^3 6x^3-4x^2-5 = 0 ----- I graphed it and found a Real solution at x = 1.223423... Cheers, Stan H.

Geometry_Word_Problems/397926: the dimensions of a rectangle are such that its length is 5 inches more than its width. If teh length were doubled and the width were decreases by 2 inches the area would be increases by 52 inches squared what are the length and width of teh rectangel 1 solutions Answer 281937 by stanbon(57395)   on 2011-01-21 16:01:00 (Show Source): You can put this solution on YOUR website! the dimensions of a rectangle are such that its length is 5 inches more than its width. If the length were doubled and the width were decreased by 2 inches the area would be increased by 52 inches squared. What are the length and width of the rectangel? --- Original dimensions: Let the width be "x". Then the length is "x+5" Area is x(x+5) = x^2+5x. -------------------------- New dimensions: width = x+2 length = 2(x+5) Area is 2(x+5)(x+2) = 2(x^2+7x+10) = 2x^2+14x+20 ---------------- Equation: New Area - Old Area = 52 sq. in. 2x^2+14x+20 -(x^2+5x) = 52 --- x^2+9x+20 = 52 x^2+8x-32 = 0 Use Quadratic formula to get a positive solution: x = 2.93 inches (width) x+5 = 7.93 inches (length) ================ Cheers, Stan H.

Geometry_proofs/397933: what kInd of process do you use to show that a statement must be true because it cannot be false ? 1 solutions Answer 281932 by stanbon(57395)   on 2011-01-21 15:48:30 (Show Source): You can put this solution on YOUR website! Indirect Proof. Cheers, Stan H.

Graphs/397931: Find the intervals where the graph of the function f(x)=x^2-4 is above the x-axis. 1 solutions Answer 281931 by stanbon(57395)   on 2011-01-21 15:47:29 (Show Source): You can put this solution on YOUR website! Find the intervals where the graph of the function f(x)=x^2-4 is above the x-axis. ---- Since the coefficient of x^2 is positive, the parabola opens up. --- Since x^2-4 = (x-2)(x+2) = 0 means the x-intercepts are x=-2 and x=+2. The vertex is inbetween -2 and +2 and is below the x-axis. So f(x) is positive in these intervals: (-inf,-2)U(2,+inf) ================================= Cheers, Stan H. =============

Complex_Numbers/397905: Express these complex numbers in standard form correct to one decimal place: If z=16(cos252°+i*sin252°) in trigonometric form find z in standard form. Thank you all for your time and assistance! -ClanMacniall 1 solutions Answer 281923 by stanbon(57395)   on 2011-01-21 15:24:17 (Show Source): You can put this solution on YOUR website! Express these complex numbers in standard form correct to one decimal place: If z=16(cos252°+i*sin252°) in trigonometric form find z in standard form. --- x = 16*cos(252) = -4.9 y = 16*sin(252) = -15.2 ----------------------------- z = -4.9-15.2i ==================== Cheers, Stan H.

Travel_Word_Problems/397922: how long to cover 92 miles traveling at 150mph 1 solutions Answer 281922 by stanbon(57395)   on 2011-01-21 15:20:14 (Show Source): You can put this solution on YOUR website! how long to cover 92 miles traveling at 150mph --- time = distance/rate --- time = 92/150 --- time = 46/75 = 36.8 minutes = 36min 48sec =========================================== Cheers, Stan H.

Square-cubic-other-roots/397928: 3^sqrt(81) 1 solutions Answer 281920 by stanbon(57395)   on 2011-01-21 15:16:24 (Show Source): You can put this solution on YOUR website! 3^sqrt(81) ------ cbrt(81) = cbrt(27)*cbrt(3) = 3*cbrt(3) ============ Cheers, Stan H.

Polynomials-and-rational-expressions/397929: Solve 4 - a-5/a+3 = a^2-1/a+3, and what does a=? 1 solutions Answer 281918 by stanbon(57395)   on 2011-01-21 15:14:31 (Show Source): You can put this solution on YOUR website! Solve 4 - a-5/a+3 = a^2-1/a+3, and what does a=? --- Multiply thru by (a+3) to get: 4(a+3) - (a-5) = a^2-1 ---- 4a+12 -a+5 = a^2-1 3a+17 = a^2-1 a^2-3a-18 = 0 ---- Factor: (a-6)(a+3) = 0 --- a = 6 or a = -3. ==== But a cannot be -3 as that would make a+3 be zero in the denominator. --- Only solution: a = 6 ========= Cheers, Stan H. =========

Polynomials-and-rational-expressions/397927: Solve 5/7+1/4=1/x, and what does x=? 1 solutions Answer 281917 by stanbon(57395)   on 2011-01-21 15:10:38 (Show Source): You can put this solution on YOUR website! Solve 5/7+1/4=1/x, and what does x=? --- lcm of 7,4,x is 28x --- Multiply thru by 28x to get: 20x + 7x = 28 27x = 28 x = 28/27 ---------- Cheers, Stan H.

Trigonometry-basics/397889: Please solve 1+3Sinx=0 Thank you 1 solutions Answer 281893 by stanbon(57395)   on 2011-01-21 13:16:56 (Show Source): You can put this solution on YOUR website! Please solve 1+3Sinx=0 3sin(x) = -1 sin(x) = -1/3 --- x = sin^-1(-1/3) = -19.47 degrees, if x is in the 4th Quadrant. If x is in the 3rd Quadrant the answer is 180+19.47 = 219.47 degrees. --------------- Cheers, Stan H.

Evaluation_Word_Problems/397886: Investing her bonus. Donna invested her $33,000 bonus and received a total of $970 in interest after one year. If part of the money returned 4% and the remainder 2.25%, then how much did she invest at each rate? Please show each step and explain what you did.. Thank you soooo much! 1 solutions Answer 281891 by stanbon(57395)   on 2011-01-21 13:12:40 (Show Source): You can put this solution on YOUR website! Investing her bonus. Donna invested her $33,000 bonus and received a total of $970 in interest after one year. If part of the money returned 4% and the remainder 2.25%, then how much did she invest at each rate? ----- Quantity Eq: x + y = 33000 dollars Interest Eq:0.04x + 0.025y = 970 dollars ------------------ Multiply thru Quantity Eq. by 4. Multiply thru Interest Eq. by 100. ------------------------------- 4x + 4y = 4*33000 4x + 2.5y = 97000 --------------------- Subtract the bottom from the top and solve for "y": 1.5y = 35000 y = $23,333.33 (amt. invested at 2.25%) --- Solve for "x": x+y = 33000 x + 23,333.33 = 33000 x = $9666.66 (amt. invested at 4%) ====================================== cheers, Stan H.

Mixture_Word_Problems/397848: The radiator in a car is filled with a solution of 70% antifreeze and 30% water. The manufacturer of the antifreeze suggests that, for summer driving, optimal cooling of the engine is obtained with only 50% antifreeze. If the capacity of the radiator is 3.5 L, how much coolant should be drained and replaced with water to reduce the antifreeze concentration to the recommended level? 1 solutions Answer 281863 by stanbon(57395)   on 2011-01-21 10:59:42 (Show Source): You can put this solution on YOUR website! The radiator in a car is filled with a solution of 70% antifreeze and 30% water. The manufacturer of the antifreeze suggests that, for summer driving, optimal cooling of the engine is obtained with only 50% antifreeze. If the capacity of the radiator is 3.5 L, how much coolant should be drained and replaced with water to reduce the antifreeze concentration to the recommended level? ---- Equation: water - water + water = water 0.30*3.5 - 0.30x + 1*x = 0.5*3.5 ---- Multiply thru by 100 to get: 30*3.5 - 30x + 100x = 50*3.5 70x = 20*3.5 --- x = 1 liter (amt. of solution that should be replaced) ============== Cheers, Stan H.

Polynomials-and-rational-expressions/397788: Divide and simplify. Simplify your answer. 1 solutions Answer 281860 by stanbon(57395)   on 2011-01-21 10:54:47 (Show Source): You can put this solution on YOUR website! [(3x-9)/(55)] / [(x-3)/(25x))] ------ Invert the denominator and multiply: ---- [(3(x-3))/(55)] * [(25x)/(x-3)] =========== Cancel the x-3 and 5 factors common to numerator and denominator to get: ----------- = [(3)/(11)] * [(5x)/(1)] --- = (15x)/11 ============== Cheers, Stan H. ============

Polynomials-and-rational-expressions/397834: A rectangle has an area given by A = x^2 + 5x + 6 Find an expression for the possible length of the rectangle. 1 solutions Answer 281849 by stanbon(57395)   on 2011-01-21 10:29:41 (Show Source): You can put this solution on YOUR website! duplicate

Polynomials-and-rational-expressions/397835: A rectangle has an area given by A = x^2 + 5x + 6 Find an expression for the possible width of the rectangle. 1 solutions Answer 281848 by stanbon(57395)   on 2011-01-21 10:28:34 (Show Source): You can put this solution on YOUR website! A rectangle has an area given by A = x^2 + 5x + 6 Find an expression for the possible width of the rectangle. --------------- Factor: A = (x+3)(x+2) ---- width could be x+3 or it could be x+2 ============= Cheers, Stan H. =============